منابع مشابه
QUASI-PERMUTATION REPRESENTATIONS OF METACYCLIC 2-GROUPS
By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus, every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fa...
متن کاملA Practical Algorithm for Finding Matrix Representations for Polycyclic Groups
We describe a new algorithm for nding matrix representations for polycyclic groups given by nite presentations. In contrast to previous algorithms, our algorithm is e cient enough to construct representations for some interesting examples. The examples which we studied included a collection of free nilpotent groups, and our results here led us to a theoretical result concerning such groups.
متن کاملGeneration of polycyclic groups
Polycyclic groups are one of the best understood class of groups. For example most of the decision problems are decidable in this class, see [7]. It seems surprising therefore that it is still an open problem whether there exists an algorithm which finds d(G) for any polycyclic group G (given by say a set of generators and relations). This is unknown even in the case when G is virtually abelian...
متن کاملOn Ordered Polycyclic Groups
It has been asserted that any (full) order on a torsion-free, finitely generated, nilpotent group is defined by some F-basis of G and that the group of o-automorphisms of such a group is itself a group of the same kind: Examples provided herein demonstrate that both of these assertions are false; however, it is proved that the group of o-automorphisms of an ordered, polycyclic group is nilpoten...
متن کاملquasi-permutation representations of metacyclic 2-groups
by a quasi-permutation matrix we mean a square matrix over the complex field c with non-negative integral trace. thus, every permutation matrix over c is a quasipermutation matrix. for a given finite group g, let p(g) denote the minimal degree of a faithful permutation representation of g (or of a faithful representation of g by permutation matrices), let q(g) denote the minimal degree of a fai...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1967
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1967-0213442-5